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In this paper, we introduce a new coarse space algorithm, the "DiscontinuousCoarse Space Robin Jump Minimizer" (DCS-RJMin), to be used in conjunction withone-level domain decomposition methods (DDM). This new algorithm makes use ofDiscontinuous Coarse Spaces(DCS), and is designed for DDM that naturallyproduce discontinuous iterates such as Optimized Schwarz Methods(OSM). Thisalgorithm is suitable both at the continuous level and for cell-centered finitevolume discretizations. At the continuous level, we prove, under someconditions on the parameters of the algorithm, that the difference between twoconsecutive iterates goes to $0$. We also provide numerical resultsillustrating the convergence behavior of the DCS-RJMin algorithm.

A Discontinuous Coarse Spaces (DCS) Algorithm for Cell Centered Finite Volumes based Domain Decomposition Methods: the DCS-RJMin algorithm